Lesson Plan Title: Transformation of Quadratic Functions
Concept/Topic to Teach: Transformations of Quadratic Functions: vertical and horizontal shifts
Standards Addressed:
Algebra II: Algebra – 3.) Determine effects of shifts on quadratic functions.
Specific Objectives:
1. TSW write quadratic equations that have been shifted horizontally and vertically.
2. TSW graph quadratic equations that have been shifted horizontally and vertically.
Required Materials:
Graphing calculator, pencil, paper
Anticipatory Set (Lead-In):
Have students graph the following equations on their graphing calculator. These create some cool images. Discuss with students that not all graphs are straight lines J We can create different images by changing parts of equations.
y=(square root)(16-x^2) - 6
y= - (SR)(16-x^2) - 6
y=(SR)(9-x^2) +1
y= - (SR)(9-x^2) + 1
y=(SR)(4-x^2) + 3
y= - (SR)(4-x^2) +3
Discuss with students quadratic equations and how they can be anywhere on the graph. Discuss how we will discover how to translate quadratics to different parts of graphs.
Step-By-Step Procedures for Teaching the Lesson:
o Students will be paired into groups of two.
o Students will then be asked to complete the attached discovery activity.
Guided Practice/Monitoring:
- The teacher will walk around and monitor students.
- The teacher will demonstrate how to put an equation into a calculator and how to graph it.
- The teacher will check student work for accuracy.
- The teacher will assign each group of students the following assignment: Create a page of 5 different graphs. One of the graphs should be the parent function. Show how each transformation moves the graph.
Closure (Reflect Anticipatory Set):
- The teacher will show an equation that has both a horizontal and vertical shift.
- The teacher will discuss how the graph is translated.
- The teacher will preview the next lesson by getting students to brainstorm ideas of other ways that the quadratic function could be changed such as flipped, stretched, or shrunk.
Assessment Based on Objectives: -
1. TSW write quadratic equations that have been shifted horizontally and vertically with 95% accuracy.
2. TSW graph quadratic equations that have been shifted horizontally and vertically with 95% accuracy
The final project will be graded with a rubric.
Adaptations (For Students With Special Needs):
There is one autistic girl in 6th period. She does not do well with change. The day
before this lesson I will pull her aside and talk to her about the calculator and
what she can do with it. I will show her ways to graph and look at the graph. I
will also pair her with another student that does well and communicates well
with all students.
Extensions (For Advanced Students):
If more advanced students finish early, I will ask them to explore other ways to translate a quadratic function. Such as: how can you make it flip down? How can you make it wider? How can you make it narrower?
Possible Connections to Other Subjects:
Graphing data is very important in the real world. Using technology can also benefit all students.
Reflection: The only problem that I foresee is that this task may be too easy. It is kind of repetitive but it should get the point across.
Transformation of the Quadratic Function (Part A)
· Graph the quadratic function below:
o What is the vertex? ___________
o Did the graph open up or down? ___________
· Check your graph on the graphing calculator.
o Push the Y= button
o Type in
o Push the GRAPH button
o Did you graph the function correctly? __________
· The function
o We are now going to look at what happens when we change the equation.
o Note: You are looking at how the function transforms into a new function.
o Using your calculator
§ Push the Y= button
§ Keep the same
§ Go down and type the next equation:
§ Push the GRAPH button to view
§ What changed from the original graph? _________________
· What is the new vertex?
o Repeat the same steps with the following equations. Describe what happened and tell the new vertex.
1. 2. 3.
o What happens when you add ‘k’ to the function?
o Can you write an equation that would model the following situations?
§ Vertically Shift the Function up 2 ___________________
§ Vertically Shift the function up 8 ___________________
§ Vertically Shift the Function up 10 __________________
§ Vertically Shift the Function up 20 __________________
§ Vertically Shift the Function up 12 __________________
· The function
o We are now going to look at what happens when we change the equation.
o Note: You are looking at how the function transforms into a new function.
o Using your calculator
§ Push the Y= button
§ Keep the same
§ Go down and type the next equation:
§ Push the GRAPH button to view
§ What changed from the original graph? _________________
· What is the new vertex?
o Repeat the same steps with the following equations. Describe what happened and tell the new vertex.
1. 2. 3.
o What happens when you subtract ‘k’ to the function?
o Can you write an equation that would model the following situations?
§ Vertically Shift the Function down 2 ___________________
§ Vertically Shift the function down 8 ___________________
§ Vertically Shift the Function down 10 __________________
§ Vertically Shift the Function down 20 __________________
§ Vertically Shift the Function down 12 __________________
· Describe what is happening in each function below without a calculator. Which way is it shifting and by how much?
* Use a calculator to check your answers *
· The function
o We are now going to look at what happens when we change the equation.
o Note: You are looking at how the function transforms into a new function.
o Using your calculator
§ Push the Y= button
§ Keep the same
§ Go down and type the next equation:
§ Push the GRAPH button to view
§ What changed from the original graph? _________________
· What is the new vertex?
o Repeat the same steps with the following equations. Describe what happened and tell the new vertex.
1. 2. 3.
o What happens when you subtract ‘h’ from x before the function is squared?
o Can you write an equation that would model the following situations?
§ Horizontally Shift the Function Right 2 ___________________
§ Horizontally Shift the function Right 8 ___________________
§ Horizontally Shift the Function Right 10 __________________
§ Horizontally Shift the Function Right 20 __________________
§ Horizontally Shift the Function Right 12 __________________
· The function
o We are now going to look at what happens when we change the equation.
o Note: You are looking at how the function transforms into a new function.
o Using your calculator
§ Push the Y= button
§ Keep the same
§ Go down and type the next equation:
§ Push the GRAPH button to view
§ What changed from the original graph? _________________
· What is the new vertex?
o Repeat the same steps with the following equations. Describe what happened and tell the new vertex.
1. 2. 3.
o What happens when you add ‘k’ to x before the function is squared?
o Can you write an equation that would model the following situations?
§ Horizontally Shift the Function Left 2 ___________________
§ Horizontally Shift the function Left 8 ___________________
§ Horizontally Shift the Function Left 10 __________________
§ Horizontally Shift the Function Left 20 __________________
§ Horizontally Shift the Function Left 12 __________________
· Describe what is happening in each function below. Which way is it shifting and by how much?
* Use a graphing calculator to check *
· Combinations
o Write the equation that describes the transformation.
1. Shift up 2 and to the right 4: ______________________
2. Shift down 3 and to the right 5: ______________________
3. Shift up 1 and to the left 1: ______________________
4. Shift down 5 and the left 6: ______________________
5. Shift up 7 and to the left 6: ______________________
6. Shift down 5 and the right 1: ______________________
7. Shift up 4 and to the right 6: ______________________
8. Shift down 10 and to the right 2: ______________________
9. Shift up 6 and the left 4: ______________________
10. Shift down 11 and to the right 6: ______________________